Presentation Transcript

1. Considerations towards an Effective Bin DesignChet SparksAdaora JohnsonMatthew MilanowskiAnas Al RabbatMichael McClurg
2. OBJECTIVES Understand the Problems of Bulk Solid Flow Create Matlab Programs That Aid In Calculations Understand the Components of Effective Bin Design Perform Calculations Related to Bin Design http://bulksolidsflow.com.au/ http://eng.tel-tek.no/Powder-Technology/Silo-design-and-powder-mechanics/Silo-design-based-on-powder-mechanics-overview http://www.fil.ion.ucl.ac.uk/spm/software/spm8/
3. key points to consider when designing bins Storage capacity: Always keep in mind the amount of material that you are going to store because that will effect how many bins you will need to design. The location of the bin will also effect the design. Discharge Frequency & rate: How much time will the solid remain without contact? Around what range will the instantaneous discharge rate be? Does the rate depend on weight or on the volume? What is the required feed accuracy? http://jenike.com/files/2012/10/BlueSiloCollapsing-41.jpg http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
4. key points to consider when designing bins Temperature and Pressure: Will the material be at a low or high temperature than it’s surroundings? Is the material being fed into a positive or negative pressure environment? Fabrication Materials: Is the solid abrasive or corrosive? Will there be need for corrosion-resistant alloys? Are ultrahigh-molecular-weight plastic liners tolerable? Is the application subject to any regulatory compliance requirements? Safety and environmental considerations: Are there any safety environmental issues like material explosive ability or maximum dust composer limits? Bulk solid uniformity: What is the required material uniformity ( eg: size, shape, moisture content) How will particle segregation affect production and the final product? http://www.proagro.com.ua/eng/research/grain/4064511.html http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
5. Void Understand Bulk-solids flow problems Arching or Bridging: This is when a no-flow condition occurs in which a material forms a stable bridge/dome across the outlet of a bin. Ratholing: Another no-flow condition in which material forms a stable open channel within the bin resulting in erratic flow to the downstream process. Flooding or flushing: a condition in which an aerated bulk solid behaves like a fluid and flows uncontrollably through an outlet or feeder. Flowrate limitation: Insufficient flowrate, typically caused by counter-flowing air slowing the gravity discharge of fine powder. Particle segregation: segregation may prevent a chemical reaction, cause out of spec product, or require costly rework. Capacity: As low as only 10-20% of the bins rated storage capacity. Arching Ratholing http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
6. Measure the flow properties of the bulk solid The purpose of measuring the flow properties is mainly in order to control how the fluid would behave in a bin. The table shows the most important bulk-solid handling properties. Variables that affect solid parameters: Moisture content Particle size, shape, and hardness Pressure Temperature Storage time at rest Wall surface Chemical additives http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
7. Calculate The Approximate Size Of The Bin The above equation is used to find the height of the cylinder section needed to store the desired capacity. This design process is iterative. H: Height m: the mass in Kg. A: the cross-sectional area of the cylinder. ρavg: Average bulk density in (kg/m^3) Due to the volume lost at the top of the cylinder which is due to the bulk solid’s angle of repose and along with the volume of material in the hopper section , a reasonable sufficient estimate for the height can be found by keeping the height of the bin between one and four times the diameter or width since values out of that range are most often uneconomical. http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
8. Type of Flow Patterns- Funnel Flow Bulk solids flow much differently than liquids in tanks. A liquid would flow in a first-in/first-out sequence, but many bins have flows in a funnel-flow pattern. Funnel-flow is defined as when some of the material flows in the center of the hopper while the rest remains stationary along the walls. Funnel-flow is the most economical choice if the bulk solid is nondegradable, coarse, free-flowing, and if the segregation during discharge is not an issue. Funnel Flow Discharge http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
9. Type of Flow Patterns- Mass Flow Many problems can occur when there is funnel-flow. Some problems include ratholes, arches, caking, equipment failure, etc… Mass-flow occurs when all the material moves when any is discharged. Mass-flow bins work well with powders, cohesive materials, materials that degrade with time, and whenever sifting segregation must be minimized. Mass Flow Discharge http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
10. Designing for Mass Flow The converging hopper section must be steep enough, the wall surface friction low enough, and the outlet large enough to allow a flow without stagnant regions. This will also help prevent arching. In order to determine the wall friction angle, various wall surfaces are powder tested. These tests are conducted using a direct shear tester along the lines of ASTM D-6128. Sand will require a steep hopper angle in order to achieve mass flow because it is a highly frictional bulk solid. Smooth catalyst beds will achieve mass flow at a relatively shallow hopper angle because it is a low-friction bulk solid. http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf http://www.dietmar-schulze.com/storage.html
11. Designing for Mass Flow To prevent arching you must measure the cohesive strength of the material you want to transport. First the flow function of the material, the is measured in a laboratory test according to ASTM D-6128 with a direct shear tester. Just like in the wall friction test, consolidating forces are applied to a material. In the test cell, the force required to shear the material is measured. Minimum outlet sizes needed to avoid arching can be calculated once the flow function is determined. http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf http://www.dietmar-schulze.com/storage.html
12. This equation can be used to approximate the maximum discharge rate from a converging hopper. This can only be used if the bulk material is coarse and free-flowing. In order for a material to be considered coarse, the particles must have a diameter of at least 3 mm (1/8 in). An example of this scenario is on the next slide. In the above equation, the variables are defined as: M: mass flow rate (kg/s) ρ: bulk density (kg/m3) A: outlet area (m2) g: acceleration (m/s2) B: outlet size (m) θ: mass-flow hopper angle measured from vertical (deg.) m: outlet parameter dependent on type of hopper For conical: m = 1 for a circular outlet For wedge-shaped: m = 0 for a slot-shaped outlet http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
13. Types of Bulk Solids Mass flowing bulk solids Does not follow mass flow equations This equation only works for coarse and free-flowing material because it neglects the material’s resistance to airflow. For example, the equation would not correctly estimate the flow rate for a fine powder. The fine powder would have particles with diameters much less than 3 mm and would be greatly affected by airflow. Thus, the equation would give an answer that is much greater than the true value for the mass flow rate. http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf http://upload.wikimedia.org/wikipedia/commons/9/98/Rhodium_powder_pressed_melted.jpg
14. Function That Calculates Mass Flow Rate function [ M ] = DischargeRate( rho,A,g,B,theta,m ) % DischargeRate: Approximates the maximum discharge rate from a converging % hopper. % For this function to be accurate, one must assume that the bulk material % is both coarse and free-flowing, such as plastic pellets. % Input: % rho = bulk density (kg/m^3) % A = outlet area (m^3) % g = acceleration (m/s^2) % B = outlet size (m) % theta = mass flow hopper angle measured from vertical (deg.) % m = 1 for a circular outlet and m = 0 for a slot shaped outlet % Output: % M = mass flowrate (kg/s) M=rho*A*sqrt((B*g)/(2*(1+m)*tan(theta*pi/180))); end
15. Results The first answer is for a circular outlet. The second answer is for a slot-shaped outlet with the same parameters. >> DischargeRate(10,1,9.81,1,60,1) ans = 11.8994 >> DischargeRate(10,1,9.81,1,60,0) ans = 16.8283 http://www.inti.gob.ar/cirsoc/pdf/silos/SolidsNotes10HopperDesign.pdf
16. FLOW RATE VS HOPPER ANGLE
17. The previous plot compares the two shapes of outlets and also the mass flow with respect to a changing hopper angle. As the plot shows, the slot-shaped outlet has a larger mass flow for all values of the hopper angle than the circular outlet. The part of the graph between 20° and 70° is where a realistic hopper angle would exist. In this region, an increasing θleads to a decrease in mass flow. Essentially as the slope of the bin decreases, less mass exits the bottom of the bin per unit time.The code that created the plot is given below: % Creates a graph that shows the comparison of circular and slot-shaped % outlets. The mass flow rates are plotted versus the mass flow hopper % angle measured from vertical. % rho = bulk density (kg/m^3) rho=10; % A = outlet area (m^3) A=1; % B = outlet size (m) B=1; % g = acceleration (m/s^2) g=9.81; % The values for theta are from 1 degree to 90 degrees. theta=(1:1:90); % Mc = mass flow rate for a circular outlet (kg/s) Mc=rho*A*sqrt((B*g)./(2*(1+1)*tan(theta*pi/180))); % Ms = mass flow rate for a slot-shaped outlet (kg/s) Ms=rho*A*sqrt((B*g)./(2*(1+0)*tan(theta*pi/180))); plot(theta,Mc,'-b',theta,Ms,'--r') title('Comparison of Outlets') xlabel('mass flow hopper angle measured from vertical (deg.)') ylabel('mass flowrate (kg/s)') legend('Circular','Slot-shaped')
18. Designing for Funnel Flow The main factors for funnel flow are making the hopper slope steep enough to be self-cleaning, and sizing the hopper outlet large enough to overcome arching and ratholing. For the bin to capable of self-cleaning, the hopper slope must be 15-20 degrees steeper than the wall friction angle, assuming that a rathole has not formed. Knowledge of the material’s cohesive strength and internal friction is needed in order to determine the minimum dimensions to overcome ratholing and arching. For funnel flow, the design of the mass-flow bins is independent of scale, but the overall size matters. Thus, large funnel flow bins have a higher ratholing tendency, while mass flow bins have no chance of ratholing. Flow Channel Non-flowing region http://research.che.tamu.edu/groups/Seminario/numerical-topics/Bin%20Design.pdf
19. Experimental Flow Calculations: Unfortunately, some fluids have properties that can make flow calculations difficult. In these cases, collecting experimental data and interpolating can be the next best thing. For example, this data was generated to simulate storing a very viscous, “shear-thickening”, non Newtonian fluid. This liquid rapidly thickens and becomes more adhesive when exposed to a high pressure gradient. While the exact calculations are beyond the scope of this project, the data shows that at any angle less than 30 degrees from vertical, flow rate drops rapidly as the fluid hardens into a gooey solid. The question is, how do we model this flow and find a theoretical maximum rate?
20. Experimental Flow Cont. We use splines to interpolate the data and provide a model fit. Our matlab code was: Our graph provides estimated flow valuesat any angle from 5 to 50 from vertical. It shows our theoretical maximum flow isaround 90 in^3/s at approx 32 degreesfrom vertical. AN=[5 10 15 20 25 30 35 40 45 50];F=[4.1 4.7 6.1 8.2 27.3 86.2 80.3 76.4 66.1 54.1]; EF=spline(AN,F,linspace(5,50,250)); ANE=linspace(5,50,250); plot(ANE,EF);hold on;plot(AN,F,'*k'); xlabel('Angle from vertical'),ylabel('flow rate (in^3/s)'),title('Experimental flow calculations') legend('Experimental fit','Table values')
21. Rathole Calculations Ratholes can cause serious problems with flow. To better understand the issues they cause, this function calculates the fraction of usable flow area left by a rathole, and the fraction of the total volume of the bin the rathole takes up. It makes the assumption that you are using an economically designed (H=(1:4)*max diameter) cylindrical hopper with a centered cylindrical rathole and a circular outlet. Additionally, it assumes the material is not significantly large and has negligable tendency to clump together. The function is as follows: function [FA,FV]= Rathole(DI,DO,Hbin,DR,BA); %Inputs: %DI is the input diameter, or the diameter of the cylindrical bin %DO is the output diameter, or the diameter of the circular outlet %Hbin is the height of the cylindrical bin area %DR is the diameter of the rathole %BA is the bin angle in degrees. %Outputs %FA is the usable fractional area of the outlet for flow %FV is the fraction of the total volume of the bin the rathole takes up %In function %AI,AO,RA are the input, output, and rathole area %HC and HT are the height of the conical bottom section and the total area %Vtotal and VR are the total volume of the bin and the rathole volume
22. Rathole Function Continued: if Hbin<DI | Hbin>4*DI, error('Bin height should be 1 to 4 times bin diameter to be economical.') end if DR > DO | DO > DI, error('Diameters should be: DI>DO>DR') end %Our article stated that H should be DI*(1-4); this step checks that condition and other logical conditions AI=pi.*DI.^2./4;AO=pi.*DO.^2./4;RA=pi.*(DR.^2)./4; %This step calculates the input, output, and rathole area. UA=AO-RA; %This step computes the usable area by subtracting rathole area from output area. FA=UA./AO; %The fractional area is computed by dividing the usable area by the output area. HC=(DI-DO)./2.*tand(BA);HT=HC+Hbin; %The height of the bottom section is computed by the slope of the bin and the difference of the %input and output diameters, assuming the bottom section is approximately a frustrum of a cone. Vtotal=pi.*HC./3.*(DI.^2+DO.*DI+DO.^2)+AI.*Hbin; %The volume total is a combination of the formula for the volume of a %cylinder for the top combined with the volume of the bottom frustrum. VR=HT.*RA; %The volume of the rathole is calculated by multiplying the bin’s total height by the rathole’s area. FV=VR./Vtotal; %The fractional volume of the rathole is calculted by dividing the rathole volume by the total volume.
23. Example Rathole Calculations Assuming a bin with a 10 foot diameter inlet, a cylindrical bin height of 25 ft before the conical section,a bin angle of 60 degrees from horizontal, and a varying output diameter, this graph shows the effect of ratholes on fractional output area. As you can see, even smallratholes cause immediatedrops in the usable flow area,even when the output diameteris very large (1/2 inlet diameter) While it is not shown, thefraction of the total volumetaken up by these ratholesis very low; the maximum wasjust over 20% for a ratholethat was 5 ft across, or halfthe diameter of the input. For outlets that are smallfractions of the inlet diameter,less than 5% of the total volumewill cause near complete lossof usable flow area
24. Janssen Calculations: The Janssen equation, as seen in (CITE OTHER POWERPOINT HERE), calculates the pressure on a bin as a factor of bin major diameter, bin height, gravity, material density, Janssen coefficient, and bin angle from vertical. *INSERT FIGURE WITH EQUATION HERE* But what if we know the maximum pressure our bin can support, but want to figure out the minimum deviation from vertical our bin can support? We can use Matlab’sfzeroes function, the Janssen equation, and our maximum pressure to solve for the minimum angle from vertical. function AD = Amin(D,H,y,g,K,pmax); %This function calculates the minimum angle from the vertical a hopper must be using the Janssen equation. %The function calculates angle using US units. % We use .8 pmax in our calculations as a safety factor, so that fluctuations during use do not go over our maximum tolerance. %D=Diameter, H=Height, y=density, g=gravitational acceleration %K=Janssen coefficient,pmax=max pressure %AD is the minimum bin angle from vertical in degrees. AD=fzero(@(x) ((y.*g.*D./(4.*tand(x).*K)).*(1-exp(-4.*H.*tand(x).*K./D))-.8.*pmax),45); %This finds the zeroes of an anonymous Janssen function of angle, minus the (practical) pmax. %It guesses an intermediate angle of 45 degrees to start. if AD>70, error('Pmax is too low to be practical') elseif AD<0,error('Pmax is high enough angle is irrelevant.') end %These statements alert you if your Pmax is so low as to be impractical (bin angle nearly horizontal) %or too high to be practical (your bin can support being near completely vertical). AD;
25. Example Janssen Using our Janssen equation from before, we can show the minimum angle from vertical for some example bins of varying diameter and max pressure. Our example bins have a material of density 35 lb/ft^3, Janssen coefficient of .4, gravity of 32.2 ft/s^2,and a constant height of fifty feet. Code to generate graphs: for i=1:325 P(i)=5000+(i-1)*200; AD1(i)=Amin(14,50,35,32.2,.4,5000+(i-1)*200); AD2(i)=Amin(12,50,35,32.2,.4,5000+(i-1)*200); AD3(i)=Amin(10,50,35,32.2,.4,5000+(i-1)*200); AD4(i)=Amin(8,50,35,32.2,.4,5000+(i-1)*200); AD5(i)=Amin(6,50,35,32.2,.4,5000+(i-1)*200); end %A for loop is required because Matlab’sfzero function,which is used in Amin, does not support using arrays. plot(P,AD1);hold on; plot(P,AD2,'r') plot(P,AD3,'g') plot(P,AD4,'k') plot(P,AD5,'c'); xlabel('Absolute Maximum Pressure (psi)') ylabel('bin angle from vertical (degrees)') title('Maximum pressure versus angle at various diameters') legend('D= 14 ft','D= 12 ft','D= 10 ft','D= 8 ft','D= 6 ft')
26. A rectangular straight sided section at the top of the bin is preferred over a circular cross-section, because it is easier to construct and has a larger cross-sectional area per unit height. DEVELOPING THE OVERALL BIN GEOMETRY Rectangular Silo Circular Silo http://krishnagrainsystems.co.in/Compartmental%20Silo.html
27. However, flat walls are susceptible to bending unlike a cylinder that has hoop tension that can support greater internal pressure. DEVELOPING THE OVERALL BIN GEOMETRY The stresses around the wall balance the internal pressure across the cross section. Rectangular shaped bin that succumbed to overloading. Static equilibrium between the total hoop stress σh and pressure p. http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfm http://singcore.com/images/MetalCrunched2txt.jpg
28. Rectangular bins also have corners where the material may build up. DEVELOPING THE OVERALL BIN GEOMETRY http://www.emeraldinsight.com/content_images/fig/1820300201017.png
29. 5 Considerations to Have When Choosing a Hopper
30. How Much Headroom is Available Wedge and pyramidal shapes can be made less steep than conical and transition shapes 10 Steps to an Effective Bin Design Article
31. Outlet Size Conical hoppers must have an outlet diameter of twice the outlet width a wedge shaped hopper (provided that the outlet length is 3 times the width) in order to avoid developing cohesive or interlocking arches during transport. Cones generally require larger feeders http://www.scielo.br/scielo.php?pid=S0100-69162013000300003&script=sci_arttext
32. Discharge Rate Slot outlets generally have a larger cross-sectional area than circular outlets so they provide larger flowrates A depiction of various flowrates of material through a silo http://www.friedrich-electronic.com/applications/blending/free-flowing-products/
33. Sharp VS Round Corners Conical and transition hoppers don't have corners which allows material build-up. Pyramidal Hoppers cause funnel flow problems because of their in-flowing valleys which are less steep than the adjacent side walls. http://www.chemicalprocessing.com/articles/2002/94/
34. Capital Cost:Conserving Your Cash Depending on the shape of your silo, costs will vary many areas. For instance, wedge shapes require less headroom and thus less material and money. However, feeders and gate valves for wedge shapes may be more expensive. http://24.media.tumblr.com/a51c48a643929194ce44d0594291aaa0/tumblr_mqua3ubkKx1rjcfxro1_500.gif
35. 3 Common Types of Bulk Solids Feeders SELECTING THE OUTLET FEEDER
36. Screw Feeders Use these with hoppers that have elongated outlets. These feeders are totally enclosed, making them perfect for use with dusty material. There are few moving parts to manage. The key to an effective screw feeder design is a tapered cut and an increase in capacity in the direction of feed. 10 Steps to an Effective Bin Design Article
37. Belt Feeders Belt feeders are good for elongated hopper outlets and great for handing cohesive and bulk solids that require a high discharge rate. They’re not good for handling dusty materials because of the lack of containment. They can also be equipped to perform gravimetric operations (weighing the material it transports). The key to a proper belt feeder is an increasing capacity in the direction feed 10 Steps to an Effective Bin Design Article
38. Rotary Valves These are used with hoppers that have square or circular outlets. These cannot handle highly cohesive solids, because bridges are likely to form. Interfaces are used with both these and belt feeders to ensure that solids are withdrawn uniformly across the entire hopper outlet. Without this interface, a preferential flow channel may develop on the side on the side of the hopper outlet, which results in non-uniform discharge. Shown above is a rotary valve feeder to the left and a blueprint of its in workings to the right http://www.mikropul.com/index.php/products/details/rotary_airlocks
39. Outlet Gate or Shut-Off ValveFunctional Components The outlet gate is not needed to regulate flow rate, but instead it should be used for maintenance only. Outlet gates or valves should be either fully open or fully closed. This is a slide gate valve operated pneumatically for rapid action. These gates can also be operated hydraulically for power or electronically for precision and timing. http://www.dclinc.com/product-profile/14/19/ http://www.pneuvay.com.au/images/pneuvay-vortex-abrasive-duty-gate.jpg
40. Number of OutletsFunctional Components Multiple outlets are attractive for production flexibility, but they can have severe consequences structurally and from a flow perspective. A single outlet will be enough to finish the desired task of the bin. CLICK A single outlet bin will allow for a more structurally sound design, but it will only permit for production of one material. http://www.metalfabinc.com/images_pages/bin_activ.gif
41. Bin Vent or Dust CollectorFunctional Components Depending on the method used, an air-solid separator may be needed. Dust particles are highly explosive in a closed area and need to be removed from the product. Aftermath of a dust explosion. High concentrations of dust in a closed area causes rapid combustion. http://media.syracuse.com/news/photo/2010/04/2010-04-12-gw-silo004jpg-16f57a8db1f3b6e9_medium.jpg
42. Conservation VentFunctional Components Needed for thin-walled steel hoppers. These vents help relieve excess pressure and prevent vacuum conditions which will cause damage to the structure of the bin. Cross-section of a conservation vent. http://www.protectoseal.com/vaporFlame/vfVacuumRelief.cfm
43. Level DetectorsFunctional Components Two different types of level detectors: Point level detection: Attached to the side wall or roof of the bin Measure solids by direct contact using capacitance sensors or pressure diaphragms Continuous level detection: Attached to the roof of the bin Emits radar or ultrasonic signals to measure the surface of the material Continuous level detector (radar) http://img.directindustry.com/images_di/photo-g/tdr-guided-wave-radar-level-sensors-16712-4346365.jpg
44. MaintenanceFunctional Components Access doors Manways Poke Holes Ladders, railways, and platforms: minor details for easy maintenance These accessories help make the bin accessible for maintenance and cleaning. These items need to be strategically placed in order to not hinder the flow rate of the material.
45. MetalSMaterial of construction Metal silos are made from carbon steel, stainless steel, or aluminum. Listed below are some advantages metal silos have over concrete silos: Flexible fabrication - can be constructed in the shop or the field Sanitary construction – metals can be used for food products or pharmaceuticals Wide variety of materials – many different metals exist to create the silo Construction flexibility – can be constructed in most environments (freezing precludes concrete construction)
46. ConcreteMaterial of construction Most commonly used for silos with diameters greater than 9 meters because it allows for greater stability when processing larger volumes of materials. Listed below are the advantages of a concrete silo over a metal silo: Corrosion resistance – require less maintenance Resistance to abrasion – withstand impact loads better Withstand internal pressures – resist localized buckling No need for paint – corrosion of metal silos will require periodic repainting Lower cost for large diameters – metal silos require thicker walls for large diameters
47. Conclusion This bin design process has been used for the last half century, and has been able to effectively handle bulk solids in everything from chemical powders to biomass. It is important to design the bin to meet the needs of the material being produced or stored in order to maintain efficiency, but more importantly safety. In the future scientists could develop computer programs that automatically design bins based on parameters that you input yourself such as the type of bulk solid, the state the solid is in, and the amount of solid present. http://mycomsats.com/blogs/software-engineering-universities-in-pakistan/
48. Bin Design Can Be Easy So Long as You Remember These Steps Define Storage Requirements Understand Your Bulk Solids Flow Measure Your Material’s Flow Properties Calculate the Size of Your Bin Determine Flow Patterns Design the Hopper's Geometry Develop the Overall Bin Geometry Select the Outlet Feeder Select Other Necessary Components Choose the Construction Material http://www.cgtrader.com/3d-models/architectural-exterior/industrial/cement-silo-unibeton-79-m3 http://www.wired.com/insights/2013/02/tear-down-old-silo-walls-in-the-new-enterprise/